A chain tensioning device of this kind, known from German Utility Model specification No. 78 09 294, has a tensioning head subjected to the pressure of three cylindrical springs arranged in its interior. The springs can be locked individually by means of screws, and a housing serves as a guide for the tensioning head. The pressure exerted on the chain by this chain tensioning device is not uniform over its whole range of movement, since the resilient pressure decreases as the extension increases; its guides can become dirtied and finally blocked if dirt gets into the guide housing; and above all a tensioning device of this kind, and thus also the chain, is caused to oscillate if a shock force acts on the chain.